Serra Albo, Oriol
Total activity: 268

## Scientific and technological production Ordered by:  Date asc. Date desc. Title asc. Title desc. Researcher asc. Researcher desc.

1 to 50 of 268 results
• On the tree-depth of random graphs

Perarnau Llobet, Guillem; Serra Albo, Oriol
Discrete applied mathematics
Date of publication: 2014-05-11
Journal article

Tree-depth is a parameter introduced under several names as a measure of sparsity of a graph. We compute asymptotic values of the tree-depth of a random graph on n vertices where each edge appears independently with probability p. For dense graphs, np -> +infinity, the tree-depth of a random graph G is aas td(G) = n - O ( root n/p). Random graphs with p = c/n, have aaslinear tree-depth when c > 1, the tree-depth is (-)(log n) when c = 1 and (-) (log log n) for c < 1. The result for c > 1 is derived from the computation of tree-width and provides a more direct proof of a conjecture by Gao on the linearity of tree-width recently proved by Lee, Lee and Oum (2012) [15]. We also show that, for c = 1, every width parameter is aasconstant, and that random regular graphs have linear tree-depth. (c) 2012 Elsevier B.V. All rights reserved.

• Counting patterns in colored orthogonal arrays

Montejano Cantoral, Amanda; Serra Albo, Oriol
Discrete mathematics
Date of publication: 2014-02-28
Journal article

Let S be an orthogonal array OA(d, k) and let c be an r-coloring of its ground set X. We give a combinatorial identity which relates the number of vectors in S with given color patterns under c with the cardinalities of the color classes. Several applications of the identity are considered. Among them it is shown that every coloring of an orthogonal array OA(d, d - 1) contains a positive proportion of almost rainbow vectors and also of almost monochromatic vectors of every color. (C) 2013 Elsevier B.V. All rights reserved.

• Random combinatorial structures with low dependencies: existence and enumeration.

Perarnau Llobet, Guillem
Defense's date: 2013-10-01
Universitat Politècnica de Catalunya
Theses

• Inverse additive problems for Minkowski Sumsets II

Freiman, Gregory A.; Grynkiewicz, David; Serra Albo, Oriol; Stanchescu, Y.V.
Journal of geometric analysis
Date of publication: 2013-01
Journal article

• A structure theorem for small sumsets in nonabelian groups

Serra Albo, Oriol; Zemor, Gilles
European journal of combinatorics
Date of publication: 2013-11
Journal article

Let G be an arbitrary finite group and let S and T be two subsets such that |S| = 2, |T| = 2, and |T S| = |T| + |S| - 1 = |G| - 2. We show that if |S| = |G| - 4|G|1 / 2 then either S is a geometric progression or there exists a non-trivial subgroup H such that either |H S| = |S| + |H| - 1 or |S H| = |S| + |H| - 1. This extends to the nonabelian case classical results for abelian groups. When we remove the hypothesis |S| = |G| - 4|G|1 / 2 we show the existence of counterexamples to the above characterization whose structure is described precisely.

• The Dicks-Ivanov problem and the Hamidoune problem

Dicks McLay, Warren; Serra Albo, Oriol
European journal of combinatorics
Date of publication: 2013-11
Journal article

We report on what we call the Hamidoune problem, inspired by a problem by Dicks and Ivanov. The problem asks if the inequality holds when A and B are finite subsets of a group G, each one with at least two elements, and A·2B denotes the set of elements which can be written in at least two different ways as a product of one element in A and one in B.

• Rainbow perfect matchings in complete bipartite graphs: existence and counting

Perarnau Llobet, Guillem; Serra Albo, Oriol
Combinatorics probability and computing
Date of publication: 2013-09
Journal article

A perfect matching M in an edge-coloured complete bipartite graph Kn,n is rainbow if no pair of edges in M have the same colour. We obtain asymptotic enumeration results for the number of rainbow perfect matchings in terms of the maximum number of occurrences of each colour. We also consider two natural models of random edge-colourings of Kn,n and show that if the number of colours is at least n, then there is with high probability a rainbow perfect matching. This in particular shows that almost every square matrix of order n in which every entry appears n times has a Latin transversal.

• On the removal lemma for linear systems over Abelian groups

Král, Daniel; Serra Albo, Oriol; Vena, Lluis
European journal of combinatorics
Date of publication: 2013-02
Journal article

• Yahya Ould Hamidoune's mathematical journey: a critical review of his work

Plagne, Alain; Serra Albo, Oriol; Zemor, Gilles
European journal of combinatorics
Date of publication: 2013-11
Journal article

We present the mathematical work of Yahya Ould Hamidoune, emphasizing his main achievements, notably in graph theory and additive combinatorics.

• Remarks on the equality case of the Bonnesen inequality

Böröczky, Károly J.; Serra Albo, Oriol
Archiv der mathematik
Date of publication: 2012-08
Journal article

• Inverse additive problems for Minkowski sumsets I

Freiman, Gregory A.; Grynkiewicz, David; Serra Albo, Oriol; Stanchescu, Y.V.
Collectanea mathematica
Date of publication: 2012-09
Journal article

• Rainbow-free 3-colorings of abelian groups

Montejano Cantoral, Amanda; Serra Albo, Oriol
Electronic journal of combinatorics
Date of publication: 2012-02-23
Journal article

• A removal lemma for systems of linear equations over finite fields

Král, Daniel; Serra Albo, Oriol; Vena, Lluis
Israel journal of mathematics
Date of publication: 2012-01
Journal article

• On the cardinality of sumsets in torsion-free groups

Böröczky, Károly J.; Pálfy, P.P.; Serra Albo, Oriol
Bulletin of the London Mathematical Society
Date of publication: 2012-10
Journal article

• The Removal Lemma: algebraic versions and applications

Vena Cros, Lluís
Defense's date: 2012-07-02
Department of Applied Mathematics IV, Universitat Politècnica de Catalunya
Theses

• Yahya Ould Hamidoune, 1948--2011

Llado Sanchez, Anna; Serra Albo, Oriol; Plagne, Alain
Date: 2012-03-01
Report

• Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación

Aguilo Gost, Francisco de Asis Luis; Abiad Monge, Aida; Andrés Yebra, José Luis; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Ball, Simeon Michael; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Espona Dones, Margarida; Sau Valls, Ignasi; Montejano Cantoral, Amanda; Perarnau Llobet, Guillem; Moragas Vilarnau, Jordi; Vena Cros, Lluís; Andres Yebra, Jose Luis; Fiol Mora, Miquel Àngel
Participation in a competitive project

• On the number of monochromatic solutions of integer linear systems on Abelian groups

Serra Albo, Oriol; Vena, Lluis
Electronic notes in discrete mathematics
Date of publication: 2011-12-01
Journal article

Let G be a finite cyclic group an let r be a positive integer. Let A be a k×m matrix with integer entries. We show that, if A satisfies some natural conditions, then the homogeneous linear system Ax=0 has Ω(|GN|m−k) monochromatic solutions for each r-coloring of GN\{0} and sufficiently large N. Density versions of this counting result are also addressed.

• Rainbow Matchings: Existence and counting

Perarnau Llobet, Guillem; Serra Albo, Oriol
Electronic notes in discrete mathematics
Date of publication: 2011-12-01
Journal article

• Properties of two-dimensional sets with small sumset

Grynkiewicz, D; Serra Albo, Oriol
Journal of combinatorial theory. Series A
Date of publication: 2010-02
Journal article

• INTERNATIONAL WORKSHOP ON OPTIMAL NETWORK TOPOLOGIES

Balbuena Martinez, Maria Camino Teofila; Mitjana Riera, Margarida; Serra Albo, Oriol; Fàbrega Canudas, Josep; Comellas Padro, Francesc de Paula
Participation in a competitive project

• A mathematical model for dynamic memory networks

Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Serra Albo, Oriol; Andrés Yebra, José Luis
International Workshop on Optimal Network Topologies
Presentation's date: 2010-06-11
Presentation of work at congresses

The aim of this paper is to bring together the work done several years ago by M.A. Fiol and the other authors to formulate a quite general mathematical model for a kind of permutation networks known as dynamic memories. A dynamic memory is constituted by an array of cells, each storing one datum, and an interconnection network between the cells that allows the constant circulation of the stored data. The objective is to design the interconnection network in order to have short access time and a simple memory control. We review how most of the proposals of dynamic memories that have appeared in the literature fit in this general model, and how it can be used to design new structures with good access properties. Moreover, using the idea of projecting a digraph onto a de Bruijn digraph, we propose new structures for dynamic memories with vectorial capabilities. Some of these new proposals are based on iterated line digraphs, which have been widely and successfully used by M.A. Fiol and his coauthors to solve many different problems in graph theory.

• Asymptotic upper bounds on the generalized chromatic numbers in classes of graphs of bounded degree

Perarnau Llobet, Guillem; Serra Albo, Oriol
French Combinatorial Conference
Presentation's date: 2010-07
Presentation of work at congresses

• On the tree depth of random graphs

Perarnau Llobet, Guillem; Serra Albo, Oriol
Jornadas de Matemática Discreta y Algorítmica
Presentation's date: 2010-06-15
Presentation of work at congresses

The tree-depth of a graph G is a parameter that plays a crucial role in the theory of bounded expansion classes and has been introduced under numerous names. We describe the asymptotic behaviour of this parameter in the case of dense and of sparse random graphs. The results also provide analogous descriptions for the tree-width of random graphs.

• On the number of solutions of regular systems in sets with positive density in abelian groups

Král, Daniel; Serra Albo, Oriol; Vena, Lluis
Jornadas de Matemática Discreta y Algorítmica
Presentation's date: 2010-06-16
Presentation of work at congresses

• Connectivity of addition Cayley graphs

Serra Albo, Oriol
Journal of combinatorial theory. Series A
Date of publication: 2009-01
Journal article

• A combinatorial proof of the Removal Lemma for Groups

Kral, D; Serra Albo, Oriol; Vena, L
Journal of combinatorial theory. Series A
Date of publication: 2009-05
Journal article

• Special Issue on EUROCOMB'07: COMBINATORICS, GRAPH THEORY AND APPLICATIONS Preface

Marquez, A; Nesetril, J; Serra Albo, Oriol
European journal of combinatorics
Date of publication: 2009-10
Journal article

• Cycle codes of graphs and MDS array codes

Serra Albo, Oriol; Zemor, Gilles
Electronic notes in discrete mathematics
Date of publication: 2009-07-30
Journal article

We investigate how to colour edges of graph so that any two colours make up a spanning tree. This problem is equivalent to transforming the cycle code of a graph into a Maximum Distance Separable (MDS) array code. Adopting this graph-theoretical interpretation allows us to provide a compact description of some families of low density MDS array codes in terms of cycle codes of coloured graphs. This includes a short description of Xu et al.’s “B-code”, together with its erasure and error decoding algorithms. We also give a partial answer to Xu et al.’s question about efficient error decoding for the dual B-code. We give alternative families of MDS array cycle codes, and in passing prove that an optimal MDS array cycle code of minimum column distance 4 is given by an appropriate colouring of the Petersen graph. We introduce double array colourings which allow the decoding of column or row errors and provides a new interesting graph theoretical problem. We give infinite families of graphs which admit double array colourings.

• Punctured combinatorial Nullstellensätze

Ball, Simeon Michael; Serra Albo, Oriol
Combinatorica
Date of publication: 2009
Journal article

In this article we present a punctured version of Alon's Nullstellensatz which states that if $f$ vanishes at nearly all, but not all, of the common zeros of some polynomials $g_1(X_1),\ldots,g_n(X_n)$ then every $I$-residue of $f$, where the ideal $I=\langle g_1,\ldots,g_n\rangle$, has a large degree. Furthermore, we extend Alon's Nullstellensatz to functions which have multiple zeros at the common zeros of $g_1,g_2,\ldots,g_n$ and prove a punctured version of this generalised version. Some applications of these punctured Nullstellens\"atze to projective and affine geometries over an arbitrary field are considered which, in the case that the field is finite, will lead to some bounds related to linear codes containing the all one vector.

• Large sets with small doubling modulo $p$ are well covered by an arithmetic progression

Serra Albo, Oriol; Zémor, Gilles
Annales de l'Institut Fourier
Date of publication: 2009-10-05
Journal article

• On sums of dilates

Javier, Cilleruelo; Hamidoune, Yahya O.; Serra Albo, Oriol
Combinatorics probability and computing
Date of publication: 2009-10-05
Journal article

For k prime and A a finite set of integers with |A| ≥ $3(k-1)^2$ (k-1)! we prove that |A+k·A| ≥ (k+1)|A| − ⌈k(k+2)/4⌉ where k·A = {ka:a∈A}. We also describe the sets for which equality holds.

• Rainbow-free 3-colorings in abelian groups

Montejano Cantoral, Amanda; Serra Albo, Oriol
Electronic notes in discrete mathematics
Date of publication: 2009-07-27
Journal article

A 3–coloring of an abelian group G is rainbow–free if there is no 3–term arithmetic progression with its members having pairwise distinct colors. We describe the structure of rainbow–free colorings of abelian groups. This structural description proves a conjecture of Jungi´c et al. on the size of the smallest chromatic class of a rainbow–free coloring of cyclic groups.

• On the chromatic number of circulant graphs

Barajas Tomas, Javier; Serra Albo, Oriol
Discrete mathematics
Date of publication: 2009-09
Journal article

• Investigando las matemáticas de las redes de comunicación

Fàbrega Canudas, Josep; Serra Albo, Oriol
Date: 2009-07-13
Report

• SOME GEOMETRIC ASPECTS OF SUM SETS

Serra Albo, Oriol
Participation in a competitive project

• PROBLEMAS EXTREMALES Y DE OPTIMIZACIÓN EN TEORIA DE GRAFOS Y COMBINATORIA: APLICACIÓN AL ANALISIS Y ALGORITMOS DE REDES DE COMUNICAC

Abiad Monge, Aida; Andres Yebra, Jose Luis; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Espona Dones, Margarida; Fàbrega Canudas, Josep; Gago Alvarez, Silvia; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Montejano Cantoral, Amanda; Moragas Vilarnau, Jordi; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Perarnau Llobet, Guillem; Pérez Mansilla, Sonia; Rius Font, Miquel; Sau Valls, Ignasi; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Vena Cros, Lluís; Fiol Mora, Miquel Àngel
Participation in a competitive project

• COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

Comellas Padro, Francesc de Paula; López Masip, Susana Clara; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest; Espona Dones, Margarida; Rius Font, Miquel; Aroca Farrerons, Josep Maria; Aguilo Gost, Francisco de Asis Luis; Dalfo Simo, Cristina; Moragas Vilarnau, Jordi; Cámara Vallejo, Marc; Gago Alvarez, Silvia; Ball, Simeon Michael; Andres Yebra, Jose Luis; Pérez Mansilla, Sonia; Mitjana Riera, Margarida; Llado Sanchez, Anna; Barriere Figueroa, Eulalia; Fàbrega Canudas, Josep; Muñoz Lopez, Francisco Javier; Zaragoza Monroig, Maria Luisa; Gomez Marti, Jose; Miralles De La Asuncion, Alicia; Pelayo Melero, Ignacio Manuel; Serra Albo, Oriol
Participation in a competitive project

• Colored combinatorial structures: homomorphisms and counting.

Montejano Cantoral, Amanda
Defense's date: 2009-06-09
School of Mathematics and Statistics (FME), Universitat Politècnica de Catalunya
Theses

• On some subgroup chains related to Kneser's theorem

Serra Albo, Oriol
Journal de théorie des nombres de Bordeaux
Date of publication: 2008-10
Journal article

• The lonely runner with seven runners

Serra Albo, Oriol
Electronic journal of combinatorics
Date of publication: 2008-05
Journal article

• On s-arc transitive hypergraphs

Pérez Mansilla, Sonia; Serra Albo, Oriol
European journal of combinatorics
Date of publication: 2008-05
Journal article

• Homomorphisms: Structure and highlights - Preface

Nesetril, J; Serra Albo, Oriol
European journal of combinatorics
Date of publication: 2008-05
Journal article

• On the critical pair theory in abelian groups: beyond Chowla's theorem

Serra Albo, Oriol
Combinatorica
Date of publication: 2008-07
Journal article

• On complete subsets of the cyclic group

Hamidoune, Yahya O.; Llado Sanchez, Anna; Serra Albo, Oriol
Journal of combinatorial theory. Series A
Date of publication: 2008-10
Journal article

• European journal of combinatorics

Serra Albo, Oriol
Collaboration in journals

Serra Albo, Oriol
European Congress of Mathematics
Presentation's date: 2008-07-14
Presentation of work at congresses

• A removal lemma for linear systems

Serra Albo, Oriol
Jornadas de Matemática Discreta y Algorítmica
Presentation of work at congresses

• Punctured Combinatorial Nullstellensatz

Ball, Simeon Michael; Serra Albo, Oriol
Jornadas de Matemática Discreta y Algorítmica
Presentation's date: 2008-07-21
Presentation of work at congresses

• The lonely runner problem

Serra Albo, Oriol
Journee Theorie de Nombres
Presentation's date: 2008-11-10
Presentation of work at congresses